Model-Free Feature Screening for Ultrahigh Dimensional Data

By Liping Zhu, Lexin Li, Runze Li, Lixing Zhu. Journal of the American Statistical Association, 2011

518 citations recorded by the source corpus.

With the recent explosion of scientific data of unprecedented size and complexity, feature ranking and screening are playing an increasingly important role in many scientific studies. In this article, we propose a novel feature screening procedure under a unified model framework, which covers a wide variety of commonly used parametric and semiparametric models. The new method does not require imposing a specific model structure on regression functions, and thus is particularly appealing to ultrahigh-dimensional regressions, where there are a huge number of candidate predictors but little information about the actual model forms. We demonstrate that, with the number of predictors growing at an exponential rate of the sample size, the proposed procedure possesses consistency in ranking, which is both useful in its own right and can lead to consistency in selection. The new procedure is computationally efficient and simple, and exhibits a competent empirical performance in our intensive simulations and real data analysis.

Subfields: Artificial Intelligence, Molecular Biology, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/2ab4c69e9f46e64c93619b0662970de2625e9aef

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Citations in the corpus

Feature Screening via Distance Correlation Learning (2012, methodology): “Zhu et al. (2011) proposed an alternate method to determine d for the SIRS.”
A Statistically and Numerically Efficient Independence Test Based on Random Projections and Distance Covariance (2017, methodology): “Distance-based independence/dependence measurements sometimes have been utilized in performing a greedy feature selection, often via dependence maximization [8,30,31], and it has been effective on some real-world datasets.”
Fast Computing for Distance Covariance (2014, methodology): “Both the SIS and the SIRS have little chance to identify the important predictors X1 and X2 in models (1.b) and (1.c), and X22 in model (1.d).”
The fused Kolmogorov filter: A nonparametric model-free screening method (2014, background): “…nonparametric, have been proposed and studied in recent years [Chang, Tang and Wu (2013), Fan and Fan (2008), Fan, Feng and Song (2011), Fan, Samworth and Wu (2009), Fan and Song (2010), He, Wang and Hong (2013), Li, Zhong and Zhu (2012), Li et al. (2012), Mai and Zou (2013), Zhu et al. (2011)].”
Quantile-adaptive model-free variable screening for high-dimensional heterogeneous data (2013, methodology): “We consider two criteria for evaluating the performance as in Zhu et al. (2011).”
Sequential sufficient dimension reduction for large p, small n problems (2015, methodology): “For path I, order the predictors by using a marginal utility measure (e.g. Zhu et al. (2011) and Li et al. (2012)) by ranking from the weakest association to the strongest association, whereas, for path II, no particular ordering is necessary.”
Conditional quantile screening in ultrahigh-dimensional heterogeneous data (2015, methodology): “Compared with the finite exponential moment conditions C3 in Zhu et al. (2011), C1 in Li et al. (2012b) and B2 in Shao & Zhang (2014), as well as the bounded support condition C1 in He et al. (2013), we impose no conditions on the predictor Z , so our screening procedures are more robust with…”